Three identical particles \(P , Q\) and \(R\), each of mass \(m\), lie in a straight line on a smooth horizontal plane with \(Q\) between \(P\) and \(R\). Particles \(P\) and \(Q\) are projected directly towards each other with speeds \(4 u\) and \(2 u\) respectively, and at the same time particle \(R\) is projected along the line away from \(Q\) with speed \(3 u\). The coefficient of restitution between each pair of particles is \(e\). After the collision between \(P\) and \(Q\) there is a collision between \(Q\) and \(R\).
Show that \(e > \frac { 2 } { 3 }\)
It is given that \(e = \frac { 3 } { 4 }\)
Show that there will not be a further collision between \(P\) and \(Q\).